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# If p is a two digit prime number, what is the value of p?

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Re: If p is a two digit prime number, what is the value of p? [#permalink]
Q : If p is a two digit prime number, what is the value of p?

The question stem asks to find out a definite value for P.

Statement number 1 says :

(1) When p is divided by 4, the remainder is 3.

We can form an equation out of this .

p = 4x + 3 [ we have to keep in mind the range of x as p is a two digit number , 1 < x < 24 i.e 11 <= p <= 99 ]

Statement 1 is inconclusive to find out a single value of p. Option A,D is gone.We are left with B,C,E ,

(2) p is 2 more than multiple of 7.

This is a fancy way of saying that p has reminder of 2 when divided by 7 .

p = 7y + 2

Statement 2 is also inconclusive to find out a single value of p.

Option B is also gone .We are left with C and E .

We try combining statement 1 and 2 .

4x + 3 = 7y + 2

now we have two choices either get the value of x or y .

Since we have already invested finding the range of x , I am going to find out the value of y using x as variable

so , 4x + 3 = 7y + 2 becomes

=> y = (4x+1)/7

using the range of x derived earlier 1 < x < 24

We have to find out a integer value of y

so using x = 5 we get y = 3
x = 12 y = 7

At this point we don't need to find the value of p to mark the option E as we have ready have two values of x within range that satisfies the y.

However , lets find out the value of p for understanding purpose , substituting x in the 1st equation {23,51 .... }

Hence there is not a definite value of p . option C is eliminated .

We have the correct option E .
Re: If p is a two digit prime number, what is the value of p? [#permalink]
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